Arrhenius Behavior of the Bulk Na-Ion Conductivity in Na3Sc2(PO4)3 Single Crystals Observed by Microcontact Impedance Spectroscopy

NASICON-based solid electrolytes with exceptionally high Na-ion conductivities are considered to enable future all solid-state Na-ion battery technologies. Despite 40 years of research the interrelation between crystal structure and Na-ion conduction is still controversially discussed and far from being fully understood. In this study, microcontact impedance spectroscopy combined with single crystal X-ray diffraction, and differential scanning calorimetry is applied to tackle the question how bulk Na-ion conductivity σbulk of sub-mm-sized flux grown Na3Sc2(PO4)3 (NSP) single crystals is influenced by supposed phase changes (α, β, and γ phase) discussed in literature. Although we found a smooth structural change at around 140 °C, which we assign to the β → γ phase transition, our conductivity data follow a single Arrhenius law from room temperature (RT) up to 220 °C. Obviously, the structural change, being mainly related to decreasing Na-ion ordering with increasing temperature, does not cause any jumps in Na-ion conductivity or any discontinuities in activation energies Ea. Bulk ion dynamics in NSP have so far rarely been documented; here, under ambient conditions, σbulk turned out to be as high as 3 × 10–4 S cm–1 at RT (Ea, bulk = 0.39 eV) when directly measured with microcontacts for individual small single crystals.


■ INTRODUCTION
Li-ion conducting solid electrolytes are highly desired for new battery concepts overcoming serious safety issues of state-ofthe-art battery technologies using liquid-based electrolytes. Moreover, the use of solid electrolytes enables very high energy densities as well as chemical and electrochemical stability, which is needed for any automotive and grid storage applications. Concerns regarding the availability of mineral resources of Li, however, increase the interest in other cations such as Na. Among Na-ion conducting solid electrolytes, NASICON-based materials, with the formula Na n M 2 (XO 4 ) 3 (M = Sc, Zr, etc.; X = Si 4+ , P 5+ , etc.), are considered as one of the most promising candidates for future all solid-state Na-ion battery (ASSNIB) technologies. These solid electrolytes were discovered by Hong et al. about 40 years ago described with the rhombohedral space group (SG) R3̅ c, known as the NASICON structure. 1, 2 The structural situation in this class of material is, however, rather complicated and still not fully understood. As an example, in the case of Na 3 V 2 (PO 4 ) 3 (NVP) a phase transition sequence from an ordered monoclinic α form (space group (SG) C2/c, a = 15.1244(6) Å, b = 8.7287(3) Å, c = 21.6143 (8) Å, β = 90.163 (2)) to the classical disordered rhombohedral cell (SG R3̅ c, a = 8.73382(4) Å, c = 21.91438(17) Å) with two intermediate incommensurate modulated structures β and β′ was described. 3 A further complication arises due to the different and conflicting behavior of powders and single crystals of NASICON-materials. 4 For polycrystalline samples of Na 3 Sc 2 (PO 4 ) 3 (NSP), fabricated at high temperatures, two phase transitions are reported 5−7 with the room temperature (RT) structure often being described using a monoclinic cell with space group symmetry C2/c. 8−11 In contrast, flux grown single crystals are reported to show only a single phase transition at around 160°C from the high temperature structure with SG R3̅ c to a more complicated trigonal structure with a 2a, c supercell. 4,12,13 It has been reported that these structural changes in NASICON materials are associated with changes of the thermal activation of Na-ion conductivity. While for NSP in some papers only a single change in activation energy (E a ) associated with the α → β or β → γ phase transition is detected, in other papers, however, two changes in Na-ion conductivity were reported and assigned to the two structural changes. Some of these discrepancies in structure−property relationships published in literature seem to be related to the use of total Na-ion conductivities instead of bulk Na-ion conductivities. The total conductivity comprises both grain boundary and bulk contributions. Of course, only the latter contains intrinsic transport properties which, to our opinion, will be mostly affected by the crystal chemical changes. Hence, with the data available until now, the apparently observed jumps in the thermal activation of the conductivity cannot be unequivocally assigned to the phase transitions reported.
Extremely high bulk conductivities in the mS cm −1 range are equivalent to electrical relaxation processes with very short relaxation times. At ambient or slightly elevated temperature, the relaxation frequencies of these low resistive bulk processes with capacitances in the pF range are only seen in the MHz to GHz regime. If powder samples are examined, the presence of grain boundaries often complicates the evaluation of impedance data in Nyquist plots and may hinder an unambiguous analysis of the bulk conductivity. Moreover, chemical and structural inhomogeneities in polycrystalline samples may limit the accurate study of electrochemical properties as only mean values are accessible. The use of microelectrodes on top of single crystals, however, enables a very precise study of conductivity properties since the obtained electrochemical data usually only depend on electrical bulk properties and morphology. Therefore, they can directly be correlated with information from single crystal diffraction. Very recently, we used the same setup with microelectrodes to successfully investigate electrical bulk properties of Li 1+x Al x Ti 2−x (PO 4 ) 3 (LATP) single crystals. 14 Here, microcontact impedance spectroscopy (MC IS) is combined with single crystal X-ray diffraction (SC XRD) to study possible interrelationships between intragrain Na-ion conductivity and phase transitions of flux grown NSP single crystals. Surprisingly, contrary to the various reports in literature, we do not observe any discontinuities in Na-ion conductivity as a function of temperature.

■ EXPERIMENTAL SECTION
Synthesis of Single Crystals. Single crystals of Na 3 Sc 2 (PO 4 ) 3 were grown using the flux method as described by Sotofte and Fu. 15 First, ScPO 4 was prepared via solid state reaction from a stoichiometric amount of Sc 2 O 3 (Projector GmbH, 99.5%) and NH 4 H 2 PO 4 (Merck KGaA, 99%). The homogenized mixture was heated up with 300 K/h to 900°C for 3 h. After grinding, the powder was annealed at 1200°C for 20 h. A ratio 1:6 of ScPO 4 and Na 4 P 2 O7 (Sigma-Aldrich, 95%) was heated in a Pt crucible at 1100°C for 5 h in air, then cooled down to 900°C at 3 K/h, before the furnace was free cooled to RT. The single crystals of several hundreds of μm in size were extracted from the molten mass with hot water.
Single Crystal X-ray Diffraction. SC XRD data at RT were collected on several crystals on a Bruker SMART APEX CCDdiffractometer. Intensity data were collected with graphite-monochromatized Mo K α X-ray radiation (50 kV, 30 mA). The crystal-todetector distance was 30 mm and the detector positioned at −28°2Θ using an ω-scan mode strategy at four different ϕ positions (0°, 90°, 180°, and 270°). 630 frames with Δω = 0.3°were acquired for each run. Three-dimensional data were integrated and corrected for Lorentz-, polarization, and background effects using the APEX3 software. 16 To study the evolution of the crystal structure with temperature, three data sets (at 298, 403, and 503 K) were also collected at an STOE IPDS II single-crystal diffractometer system equipped with an image plate detector at the University of Innsbruck. Elongated exposure time of 120 s per frame and significantly finer increments of 0.1°were chosen. Intensity integration was performed with X-Area software. 17 Differential Scanning Calorimetry. The heat capacity between 0 and 300°C was measured using a power compensated PerkinElmer Diamond Differential scanning calorimetry (DSC) on samples weighing ∼38 mg. The DSC measurements were performed under a flow of Ar gas, with the calorimeter block kept at −20°C using a PerkinElmer Intracooler. Each measurement consisted of a blank run with empty calorimeter chambers, a calibration, and a sample run, where the samples were placed into the sample chamber of the calorimeter. The heat flow data (difference in heating power between the sample and the reference chamber) were collected at 100°C temperature intervals consisting of a temperature scan (heating rate of 10°C/min) and isothermal periods of 3 min before and after the temperature scan. The heat flow versus temperature data from the sample runs were shifted and rotated until the data of the isothermal periods agreed with those of the blank run. A sample-saving method for heat capacity measurements on powders using relaxation calorimetry. The data from the blank run were then subtracted from those of the sample run to give the net heat flow of the sample. For calculating the heat capacity, the net heat flow data were finally divided by the heating rate and the mass of the sample. Each sample run was corrected against a calibration run using a synthetic single crystal of corundum (31.764 mg), whose heat capacities were taken from the National Bureau of Standards Certificate. 18 The accuracy of the DSC heat capacity data was determined to be better than 0.6%.
Application of Microelectrodes on Single Crystals. For electrochemical characterization, single crystals were embedded in epoxy resin. Pt thin films were sputter deposited with a thickness of 200 nm on top of approximately 10 nm Ti (used to improve the adhesion between the sample and the electrode). Afterward a negative photoresist was coated on top of the embedded and polished single crystals. After applying the mask with the appropriate microelectrode pattern, in our case circular electrodes with a diameter of 30 μm, the samples were exposed to UV light. Areas that were covered during exposure were removed using a developer solution (Microresist Technologies, Germany). In a subsequent step the microstructure was obtained by ion beam etching.
Microcontact Solid-State Impedance Spectroscopy. The electrochemical characterization of NSP was carried out by electrical impedance spectroscopy according to ref 14. All impedance measurements were performed between RT and 200°C in a tube furnace using an Alpha-A High Resolution dielectric analyzer with a ZG-2 interface (Novocontrol, Germany) in the frequency range from 3 × 10 6 Hz to 10 2 Hz with a voltage amplitude of 100 mV. The temperature were measured using a thermocouple placed close to the single crystals. In Figure 1 the microcontact setup and a schematic picture of the performed experiment are shown.

■ RESULTS
Structural Behavior of NSP Single Crystals as Function of Temperature. In agreement with suggestions presented in literature so far, the RT SC XRD data reveal distinct superstructure reflections and cannot be indexed with a rhombohedral nor with a monoclinic cell. 4,13 This structural complexity was in the very same manner observed for dozens of single crystals, which were tested in the initial phase of our investigation. Figure 2a shows calculations of the precession images from the SC XRD data at different layers at 25°C, the peaks belonging to the R3̅ c cell are marked to highlight the superstructure peaks. The pattern cannot be indexed with the monoclinic cell, frequently encountered in literature for NSP, for example, see   12,13 To monitor possible changes of the crystal structure with temperature, we collected two data sets at elevated temper-atures. The data set collected at 130°C, that is, between the two phase transition temperatures proposed for polycrystalline samples, still shows trigonal symmetry with the only difference of somewhat weaker superstructure reflections.
Importantly, at 230°C the superstructure has completely vanished and the data can be indexed and refined with the commonly observed R3̅ c NASICON structure. Figure 2b shows the reconstructed reciprocal space layer hk1 at different temperatures, which clearly shows that the superstructure reflections disappear. The results of the refinements of the hightemperature structure are illustrated in Figure 2c and presented in Table 1.
At 503 K, the Na(1) site is occupied by ∼50%, the Na(2) by ∼70%; these estimations give rise to a total Na content of ∼2.66 per formula unit (pfu). The structure is characterized by distinct anisotropic motion of the Na atoms. The observation    (2) a Atomic coordinates (Å × 10 4 ); equivalent isotropic displacement parameters (Å 2 × 10 3 ); U eq is defined as one-third of the trace of the orthogonalized U ij tensor. of the β (most probably P3̅ cl, see above) to γ (R3̅ c) phase transition in single crystalline NSP material is further supported by DSC measurements (see Figure 3a), which show a weak and broad peak centered around 140°C. In strong contrast to the situation reported for powder samples, we found no measurable indications for the α to β phase transition for single crystals. 5 This clear difference might be caused by different synthesis conditions. To clarify this difference is beyond the scope of the present paper, which focuses on the impact of phase transformations on (bulk) ionic conductivities of NSP single crystals. As the RT structure is yet not complete resolved, no information can be extracted on Na disorder and its influence as a driving force for phase transitions. Symmetry and structural phase transitions of NSP between 100 and 500 K, as well as the role of synthesis conditions, will be presented in a follow-up paper. 19 Na-Ion Conductivity and Arrhenius Behavior of NSP Single Crystals. As an example of the impedance measurements, a Nyquist plot obtained at 23.5°C is shown in Figure  3b; in Figure 3c, the temperature dependence of σ bulk is presented. The Nyquist plot recorded at RT is composed by parts of a semicircle at high frequencies, followed by a sharp increase at low frequencies. This low frequency impedance can be attributed to the strongly ion blocking electrode and described by a resistance in parallel to a constant phase element (CPE el ) with the impedance given by Z CPE = 1/(iω) n Q, where ω is the angular frequency and the exponent n is a fit parameter accounting for nonideal behavior of the capacitance. It does not imply any mechanistic information, however, it is needed to analyze the sample-specific high frequency arc at higher temperatures. The high frequency part represents the bulk resistivity of the individual single crystals. The resistive part of the arc is approximated by a resistance element (R bulk ) and can be attributed to the volumetric Na-ion conduction σ bulk , see below. The bulk capacitance (C bulk ) of the NSP samples cannot be obtained as we have to deal with an unavoidable and high stray capacitance C stray in the order of 100 fF. The whole equivalent circuit used to analyze the impedance spectra is depicted in Figure 3b. The bulk (spreading) resistance between two circular microelectrodes with an electrode diameter d and bulk conductivity σ bulk is given by R bulk = (dσ bulk ) −1 . 20 Here we obtain σ bulk = 3.04 × 10 −4 S cm −1 at RT; this value shows almost no variation within 20 measured single crystals, the error turned out to be less than 1%.

Chemistry of Materials
σ bulk, lit. (at 49°C) is in almost perfect agreement with σ bulk = 1.70 × 10 −3 S cm −1 obtained in this study. Unfortunately, in ref 5, only activation energies E a for the total conductivity are present from which we cannot access E a, bulk . As can be seen in Figure 3c, the temperature dependence of σ bulk of three randomly selected single crystals follows an almost perfect Arrhenius behavior according to σ bulk T = A exp(−E a, bulk /k B T), where A is the pre-exponential factor of the ionic conductivity,

Chemistry of Materials
Article and k B denotes Boltzmann's constant. Up to 200°C, no change in slope of σ bulk T versus 1000/T can be observed, for E a, bulk we obtain 0.39 eV. This analysis does not take into account that true temperatures at the sample surface are slightly lower than the set temperature due to asymmetric heating.
Hence, the true activation energy might be slightly larger that 0.39 eV. Our observation that no jumps of σ bulk or changes in E a occurred contrasts with earlier studies reporting up to two changes in the thermal activation of Na-ion conduction, see Figure 3d.
As shown in Figure 3d Table 2.
Unfortunately, in most of the previous experimental reports, only the final conductivity values are presented without providing details on the procedures how source data were analyzed. At least Boehm et al. and Sorokin et al. give some information about the inability to separate bulk and grain boundary contributions at temperatures above 50°C. Their experimental setup was limited and only allowed impedance measurements up to 500 kHz, which seems to be too low to separate bulk electrical processes with fast relaxation rates. Consequently, they were restricted to use only total conductivities instead of bulk values to correlate Na-ion conductivity with structural changes. 5,24 Since the crystal chemistry of a material is usually correlated mainly to bulk properties, the use of overall conductivities could be misleading. In many cases, so far powders with μm-sized crystallites were considered and no nanostructured materials with disordered interfacial regions. Therefore, σ bulk is then expected to exceed σ g.b. ; furthermore, we would anticipate E a, bulk < E a, g.b. . If σ total represents a mixture of the two components with mutable contributions over the temperature range covered, slope changes in Arrhenius plots might be artificially generated. These changes might not show up if characteristic electric relaxation frequencies are used to evaluate conduction processes.
In our case, we did not find any convincing indications for a α → β transition of NSP single crystals grown by the flux method. Hence, we do not expect a change in σ bulk at temperatures below 120°C. Indeed, the measured bulk conductivities simply follow a straight Arrhenius line (see Figures 3c and 3d). Importantly, the β → γ phase transition, for which we in fact find indications from DSC, has no measurable impact on σ bulk . Up to 200°C the pre-exponential factor A and E a, bulk remain unchanged. A point worth mentioning is that the space groups suggested for the β and γ phase, and even for the α form, are very similar. The structural changes only result from different Na-ion ordering. 4 Of course, order−disorder phenomena may easily influence configurational and vibrational entropy contributions of the pre-exponential factor. Also activation energies of local hopping processes can change and affect long-range ion transport. Here, as far as the bulk conductivity is concerned, we exclude any significant influence of the β → γ phase transition on σ bulk of single-crystalline NSP. Finally, this finding agrees well with the singular result of Winand et al., 23 see Figure 3d. Although they studied polycrystalline samples as others, 5,21−24 they analyzed impedance data 23 recorded up to 10 MHz instead of only 500 kHz (see above). In summary, on the basis of the microcontact impedance measurements σ bulk is, if at all, only marginally influenced by the decreasing Na-ion ordering in NSP single crystals.

■ CONCLUSIONS
NSP single crystals were prepared by flux growth and investigated by SC XRD, MC IS, and DSC with respect to its crystal structure and Na-ion conduction as a function of temperature. SC XRD experiments in the suggested α (RT), β (130°C), and γ phase (230°C) regions identified at least two different modifications. The phases can be assigned to the β and γ modification, with SG P3̅ cl and SG R3̅ c, respectively. From our data, we do not find clear indications of the α phase although superlattice peaks become more intense with decreasing temperature. Instead, DSC measurements point to a single phase transition at about 140°C, which we assign to the β → γ phase transition; a possible α → β transition remains invisible in our DSC and SC XRD measurements.
The β → γ transition does not lead to discontinuities of the Arrhenius behavior of σ bulk T of NSP single crystals when investigated with microcontact impedance spectroscopy. As far as ionic bulk properties are considered, this behavior is characterized by σ bulk = 3.04 × 10 −4 S cm −1 at RT E a, bulk = 0.39 eV.

Author Contributions
The manuscript was written through contributions of all authors.   Table 2).

Chemistry of Materials
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